Upvoted. This problem is the well-studied voting problem.

there are results that for some definitions of "correct", there are no correct voting systems period.

In particular, the seminal result is Arrow's impossibility theorem, which states that no voting system satisfies all of the following criteria: (from Wikipedia)

• If every voter prefers alternative X over alternative Y, then the group prefers X over Y.
• If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged.
• There is no "dictator": no single voter possesses the power to always determine the group's preference.